The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
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Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
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-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 45
-Paragraph 2
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Amount of write-down of assets recognized in the income statement. Includes, but is not limited to, losses from tangible assets, intangible assets and goodwill.

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Goodwill and Other Intangible Assets - Additional Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Finite-Lived Intangible Assets [Line Items]
Amortization expense related to intangible assets	$ 20,829	$ 21,812	$ 18,492
Asset Impairment Charges	$ 0
Prior Period Reclassification Adjustment		$ 18,000
Customer relationships \| Maximum
Finite-Lived Intangible Assets [Line Items]
Expected remaining useful life	20 years
Customer relationships \| Minimum
Finite-Lived Intangible Assets [Line Items]
Expected remaining useful life	13 years
Patents \| Maximum
Finite-Lived Intangible Assets [Line Items]
Expected remaining useful life	20 years
Patents \| Minimum
Finite-Lived Intangible Assets [Line Items]
Expected remaining useful life	10 years
Capitalized software \| Maximum
Finite-Lived Intangible Assets [Line Items]
Expected remaining useful life	7 years
Capitalized software \| Minimum
Finite-Lived Intangible Assets [Line Items]
Expected remaining useful life	3 years